Propagation-inside-layer Expansion Research Articles

Road surface layers geometric parameters estimation by ground penetrating radar using Estimation of Signal Parameters via Rotational Invariance Techniques method

In civil engineering, ground penetrating radar is widely used to assess the roadway structures. This study evaluates the influence of interface roughness. A modified estimation of signal parameters by rotational invariance techniques algorithm is proposed with a spectral smoothing technique for efficiently estimating the time delay, the permittivity of the layers and the interface roughness. To reduce the impact of noise, a preprocessing method called propagator is used to estimate the noise variance. The algorithm is tested on simulated data obtained by the rigorous numerical method called PILE (propagation inside layer expansion). Numerical simulations are conducted to assess the performance of the algorithm. The simulation results show that the proposed algorithm can estimate road parameters with small relative root mean square error.

3-D Scattering From a PEC Target Buried Beneath a Dielectric Rough Surface: An Efficient PILE-ACA Algorithm for Solving a Hybrid KA-EFIE Formulation

An efficient hybrid KA-EFIE formulation is deployed to analyze the electromagnetic (EM) scattering from a 3-D perfectly electric conducting (PEC) object buried beneath a 2-D dielectric rough surface. In this approach, the electric and magnetic current densities on the rough surface are analytically obtained through the current-based Kirchhoff approximation (KA), whereas the electric current density on the buried object is rigorously determined by solving the electric field integral equation (EFIE) using the Galerkin’s method of moments (MoM) with Rao–Wilton–Glisson (RWG) basis functions. The KA-EFIE matrix system is then efficiently solved by the iterative propagation-inside-layer-expansion (PILE) method combined with the algebraic adaptive cross approximation (ACA). The current densities on the dielectric rough surface are thereafter used to handle the bistatic normalized radar cross-section (NRCS) patterns. The proposed hybrid approach allows a significant reduction in computation time and memory requirements compared to the rigorous Poggio–Miller–Chang–Harrington–Wu (PMCHW)-EFIE formulation which requires solving a large MoM matrix equation. Moreover, the hybridization of the ACA algorithm with the PILE method improves further the computational cost thanks to the rank-deficient propriety of the coupling matrices. To validate the hybrid approach, we compare its results with those of the rigorous PMCHW-EFIE approach.

Efficient propagation-inside-layer expansion algorithm for solving the scattering from three-dimensional nested homogeneous dielectric bodies with arbitrary shape.

This paper deals with the evaluation of electromagnetic scattering from a three-dimensional structure consisting of two nested homogeneous dielectric bodies with arbitrary shape. The scattering problem is formulated in terms of a set of Poggio-Miller-Chang-Harrington-Wu integral equations that are afterwards converted into a system of linear equations (impedance matrix equation) by applying the Galerkin method of moments (MoM) with Rao-Wilton-Glisson basis functions. The MoM matrix equation is then solved by deploying the iterative propagation-inside-layer expansion (PILE) method in order to obtain the unknown surface current densities, which are thereafter used to handle the radar cross-section (RCS) patterns. Some numerical results for various structures including canonical geometries are presented and compared with those of the FEKO software in order to validate the PILE-based approach as well as to show its efficiency to analyze the full-polarized RCS patterns.

Time delay and interface roughness estimations by GPR for pavement survey

ABSTRACTIn civil engineering, ground‐penetrating radar is widely used for road pavement surveys. In contrast to the existing literature, this paper takes account of the influence of interface roughness (surface and interlayer roughness) within the scope of data processing of radar signals. The rigorous electromagnetic method PILE (Propagation Inside Layer Expansion) provides simulated data that show the influence of the interface roughness on the backscattered primary echoes of stratified media; the interface roughness provides a continuous frequency decay of the magnitude of the echoes. The observed frequency variations of the radar magnitude introduce some shape distortion on the radar waveform. The latter variations can be modelled by an exponential function, which provides satisfactory results for a narrow bandwidth (2 GHz). An adaptation of the root‐MUSIC algorithm is proposed. As a result, it is possible to jointly estimate the time delay and the interface roughness. The algorithm is tested on data simulated by the PILE method and numerical examples are provided to assess the performance of this algorithm. The associated results show that the proposed algorithm can estimate both the time delay and roughness parameters with a small relative error.

ELECTROMAGNETIC INTERACTIONS ANALYSIS BETWEEN TWO 3-D SCATTERERS USING THE E-PILE METHOD COMBINED WITH THE PO APPROXIMATION

In this paper, the electromagnetic scattering from two scatterers is analyzed from a rigorous integral formulation solved by the method of moments (MoM). G. Kubicke has recently developed the E- PILE (Extended Propagation-Inside-Layer Expansion) method to calculate the scattering from an object above a rough surface for a two-dimensional problem. This method allows us to calculate separately and exactly the interactions between the object and the rough surface. The purpose of this paper is to extend the E-PILE method to a three-dimensional problem. Such a 3-D problem involves a large number of unknowns and can not be solved easily with a conventional method of moments by using a direct LU inversion. Thus to solve this issue, the E-PILE method is combined with the physical optics (PO) approximation to calculate the local interactions on both the object and the rough surface. By using this hybrid method, the requirements of memory and CPU time can be reduced signiflcantly.

Propagation-inside-layer-expansion method combined with physical optics for scattering by coated cylinders, a rough layer, and an object below a rough surface

In this article, the fields scattered by coated cylinders, a rough layer, and an object below a rough surface are computed by the efficient propagation-inside-layer-expansion (PILE) method combined with the physical optics (PO) approximation to accelerate the calculation of the local interactions on the non-illuminated scatterer, which is assumed to be perfectly conducting. The PILE method is based on the method of moments, and the impedance matrix of the two scatterers is then inverted by blocks from a Taylor series expansion of the inverse of the Schur complement. Its main interest is that it is rigorous, with a simple formulation and a straightforward physical interpretation. In addition, one of the advantages of PILE is to be able to hybridize methods (rigorous or asymptotic) valid for a single scatterer. Then, in high frequencies, the hybridization with PO allows us to significantly reduce the complexity in comparison to a direct lower-upper inversion of the impedance matrix of the two scatterers without loss in accuracy.

AN INVESTIGATION ON NUMERICAL CHARACTERIZATION OF SCATTERING FROM TARGET IN A DIELECTRIC ROUGH SOIL SURFACE

Based on the Propagation-Inside-Layer Expansion (PILE) and Forward-Backward method (FBM), the composite scattering from the target below a dielectric rough soil surface using the extended PILE (EPILE) combined with the Forward-Backward method (FBM) is studied. The accuracy and e-ciency of the EPILE + FBM for this speciflc type of composite scattering is researched by comparing with the method of moments (MOM), the in∞uences of the target size, target depth, target horizontal distance, the rms height, the correlation length, the incident angle and the soil moisture content, etc., to the bistatic scattering coe-cient (BSC) are also investigated.

Asymptotic Modeling of Coherent Scattering from Random Rough Layers: Application to Road Survey by GPR at Nadir

This paper studies the coherent scattering from random rough layers made up of two uncorrelated random rough surfaces, by considering 2D problems. The results from a rigorous electromagnetic method called PILE (propagation-inside-layer expansion) are used as a reference. Also, two asymptotic analytical approaches are presented and compared to the numerical model for comparison. The cases of surfaces with both Gaussian and exponential correlations are studied. This approach is applied to road survey by GPR at nadir.

THE E-PILE+SMCG FOR SCATTERING FROM AN OBJECT BELOW 2D SOIL ROUGH SURFACE

A rigorous fast numerical method called E-PILE+SMCG is introduced and then used in a Monte Carlo study of scattering from a three dimensional perfectly electrical conductor (PEC) object below lossy soil rough surface. This method is the three dimensional (3D) extendability of PILE (Propagation-Inside-Layer Expansion) method which is proposed for two dimensional (2D) scattering problem. The rough surface with Gaussian proflle is used to emulate the realistic situation of statistically rough surface, while the tapered incident wave is chosen to reduce the truncation error. The 3D angular correlation function (ACF) and bistatic scattering coe-cient (BSC) are studied and applied to the detection of a target embedded in the clutter. The ACF is computed by using numerical method with circular azimuthal angle averaging technique. Because of its success in suppressing the clutter scattering, the technique appears attractive in real life

Influence of layer roughness for road survey by ground penetrating radar at nadir: theoretical study

In civil engineering, conventional methods used to estimate the thickness of pavements assume flat interfaces. In contrast, this study uses a rigorous electromagnetic method called propagation-inside-layer-expansion (PILE) to simulate the radar backscattered signal at nadir from a rough pavement made up of two rough interfaces separating homogeneous media. The statistical distribution of the first two echoes is studied by comparison with the default flat case, together with their frequency behaviour. Within the scope of road pavement survey by ground penetrating radar, the scattering model is finally used to assess the performance of the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm, one of the well-known high-resolution time-delay estimation techniques.

Scattering by an object above a randomly rough surface from a fast numerical method: Extended PILE method combined with FB-SA

In this paper, a fast exact numerical method, based on the method of moments, is developed to calculate the scattering by an object above a rough surface. N. Déchamps et al. have recently developed the PILE (Propagation-Inside-Layer Expansion) method for a stack of two one-dimensional rough interfaces separating homogeneous media. This method allows us to calculate separately and exactly the multiple scattering contributions inside the layer. This is done with a decomposition by block of the impedance matrix (the inverse of the impedance matrix of each interface and two coupling matrices are involved). The purpose of this paper is to extend the PILE method to the more general case of two illuminated surfaces and to apply it to an object located above a rough surface. In addition, to invert a matrix of large size, the Forward–Backward Spectral Acceleration (FB-SA) approach of complexity 𝒪(N) proposed by Chou and Johnson is applied. The new method, extended PILE combined with FB-SA, is tested on Perfectly Conducting (PC) circular and elliptic cylinders located above a rough surface (dielectric or PC) obeying a Gaussian process with Gaussian and exponential height autocorrelation functions.

Scattering from very rough layers under the geometric optics approximation: further investigation

Scattering from very rough homogeneous layers is studied in the high-frequency limit (under the geometric optics approximation) by taking the shadowing effect into account. To do so, the iterated Kirchhoff approximation, recently developed by Pinel et al. [Waves Random Complex Media17, 283 (2007)] and reduced to the geometric optics approximation, is used and investigated in more detail. The contributions from the higher orders of scattering inside the rough layer are calculated under the iterated Kirchhoff approximation. The method can be applied to rough layers of either very rough or perfectly flat lower interfaces, separating either lossless or lossy media. The results are compared with the PILE (propagation-inside-layer expansion) method, recently developed by Déchamps et al. [J. Opt. Soc. Am. A23, 359 (2006)], and accelerated by the forward-backward method with spectral acceleration. They highlight that there is very good agreement between the developed method and the reference numerical method for all scattering orders and that the method can be applied to root-mean-square (RMS) heights at least down to 0.25lambda.

Fast method to compute scattering by a buried object under a randomly rough surface: PILE combined with FB-SA

A fast, exact numerical method based on the method of moments (MM) is developed to calculate the scattering from an object below a randomly rough surface. Déchamps et al. [J. Opt. Soc. Am. A23, 359 (2006)] have recently developed the PILE (propagation-inside-layer expansion) method for a stack of two one-dimensional rough interfaces separating homogeneous media. From the inversion of the impedance matrix by block (in which two impedance matrices of each interface and two coupling matrices are involved), this method allows one to calculate separately and exactly the multiple-scattering contributions inside the layer in which the inverses of the impedance matrices of each interface are involved. Our purpose here is to apply this method for an object below a rough surface. In addition, to invert a matrix of large size, the forward-backward spectral acceleration (FB-SA) approach of complexity O(N) (N is the number of unknowns on the interface) proposed by Chou and Johnson [Radio Sci.33, 1277 (1998)] is applied. The new method, PILE combined with FB-SA, is tested on perfectly conducting circular and elliptic cylinders located below a dielectric rough interface obeying a Gaussian process with Gaussian and exponential height autocorrelation functions.

Electromagnetic Scattering From a Rough Layer: Propagation-Inside-Layer Expansion Method Combined to the Forward-Backward Novel Spectral Acceleration

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, an efficient method is developed to calculate the bistatic cross section (BSC) from a stack of two one-dimensional rough interfaces separating homogeneous media. The PILE (propagation-inside-layer expansion) method recently developed by DÉchamps <etal/> was efficient with a complexity <formula formulatype="inline"><tex>${\cal O}(N^2)$</tex></formula> (<formula formulatype="inline"> <tex>$N$</tex></formula> being the number of samples per interface). To reduce this complexity, a fast method valid for a single rough surface, the forward-backward with novel spectral acceleration (FBNSA) is combined to the PILE method. Furthermore, the calculation of the coupling interactions between both interfaces are also accelerated using the NSA. The PILE-FBNSA method reaches then a complexity of only <formula formulatype="inline"><tex>${\cal O}(N)$</tex></formula>. A study of the convergence of the PILE is done and compared to the FBNSA of Moss <etal/> </para>

Electromagnetic Scattering From a Rough Layer: Propagation-Inside-Layer Expansion Method Combined to an Updated BMIA/CAG Approach

An efficient method is developed to calculate the bistatic scattering coefficient (BSC) from a stack of two one-dimensional rough interfaces separating homogeneous media. The propagation-inside-layer expansion (PILE) method recently published by Dechamps was efficient with a complexity O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) (N being the number of samples per interface). To reduce this complexity, a fast method valid for a single rough surface, the banded matrix iterative approach/canonical grid (BMIA/CAG) is combined to the PILE method. Furthermore, the calculation of the coupling interactions between both interfaces are also accelerated using a new method similar to the BMIA/CAG. The PILE method reaches then a complexity of only O(NlogN). A study of the convergence of the PILE is done and compared to another efficient method, the forward-backward.

Fast numerical method for electromagnetic scattering by rough layered interfaces: Propagation-inside-layer expansion method

Electromagnetic scattering from a stack of two one-dimensional rough surfaces separating homogeneous media is modeled with a rigorous integral formulation solved by the method of moments. We present an efficient numerical method for computing the field scattered by such rough layers, in reflection as well as in transmission. We call this method propagation-inside-layer expansion (PILE) due to its straightforward physical interpretation. To our knowledge, it is the first method able to handle problems for this configuration with a huge number of unknowns. We study the convergence of this method versus a coupling condition and validate it by comparison with results from the literature.